Coordinate conversion and vector apparatus



JUN 6 1950 R. c. DEHMEL 2,510,384

cooxnrm'rs CONVERSION ma vEc'roR APPARATUS Filed oct. 25, 1944 P/CHARD CARL DEHMEL BY Patented June 6, 1950 COORDINATE CONVERSION AND VCTOR APPARATUS melma om Dehmcl, short mus, N. J. Application October 25, 1944, Serial No; 560,288

(ci. 35'1o.2)

3 Claims. l

This invention relates to electric computing apparatus and more particularly to improved apparatus for transforming voltages representing Cartesian coordinates into voltages designating equivalent polar coordinates.

The invention applies to mechanism for indicating, according to polar coordinates, the position of a movable object, such, for example, as an airplane, ship, target, or any other object, the location or course of which must be accurately charted.

One application of the invention is to a training device adapted to simulate the flight of an aircraft with respect to the beam signals of a simulated directionalradio range. 'I'his application is illustrated herein for the purpose of describing my invention. In the referred to training device, signals are varied by mechanism operated according to the path of the simulated night and more particularly in accordance with the instant range R, and azimuth angle 6, of the simulated aircraft from a reference point and direction, respectively. The construction and design of the trainer are such that voltages are derived which vary according to the Cartesian coordinates of the instant position of the simulated aircraft along axes representing latitude and longitude. The present invention provides means whereby these Cartesian coordinate voltages may be converted to control voltages for establishing the values of R and to control said signalling mechanism.

In trainers of the type above referred to, it has been found very advantageous to also utilize polar coordinate mechanism for charting the course of the simulated aircraft because the apparatus is cheaper, more compact, and simpler than mechanism having rectilinear motions, and, it is an object of this invention to provide an improved apparatus for converting voltages representing Cartesian coordinates into control voltages determinative of the equivalent polar coordinates to operate such charting and signalling instrumentalities.

It is a further object of this invention to provide apparatus responsive to the polar coordinate control voltages to actuate mechanism according to the values of R and 0.

Another object is to provide an electro-mechanical indicating or recording device for charting any function having as parameters the polar coordinates R and 0 representing instant polar distance and angle respectively.

A feature of the invention is that Cartesian coordinate representing voltages are converted to polar control voltagesby rature windings on'both its rotor'and stator.

In accordance with this feature a vpair of Cartesian coordinate representing voltages Ex and Ey, may be transformed into control voltages having values,

' kurs: sin @ist cos mos de v Equation 1 and, Y y I lcd- PE1 cos iEy sin 0) sin d0 which correspond respectively to polar range and azimuth control voltages Er and E. to' beju'sed e as hereinafter described for establishing the magnitude of the range and the angle @representing the desired azimuth angle. The deviation from said desired angle is d0 and the terms k1 and k2 are factors of proportionality effected by'various design considerations in the rotary transformer, such as turns ratio, magnetic coupling and the like. f

A further feature of the invention-is the provision of servo-motor means controlledl by the polar azimuth control voltage to adjustthe rotary transformer to bring the azimuth control. voltage to zero and thereby determine the azimuth angle 0.

Another feature of the invention is the provision of second servo-motor means controlled by the polar range control voltage for positioningv mechanism according to the polar range.v

An additional feature of this invention resides in the use of a rotary transformer having two pairs of two-phase windings, one pair on the rotor and the other on the stator, for reducing two voltage components into a voltage representing the resultant of these components and into a control voltage for establishing the angle of the resultant with respect to a reference value.

These and other objects and features are accomplished by the invention hereinafter described and illustrated in the accompanying drawing in which: l

Fig. 1 shows a diagrammatic view of an apparatus constructed in accordance with one embodiment of 'thisinvention v means of a' sirnplet rotary transformer having two electrically quad Equation 2 source, ze, in a manner described in detail hereinafter. In Fig. 1, the rotary transformer 9, embodies two pairs of polyphase windings, one pair consisting of the two-phase windings 25 and 25' which are mounted for rotation with shaft 2, and the second pair consisting of the two-phase windings 25 and 25' which are stationary. Voltage at windings 25 and 25? is transmitted by brushes 21, 21' and 21" through rings 28, 28' and 28", respectively. Brush 21 is grounded through lead 40. The windings 26 and 25 are energized by voltages Ex and Ey each having a parameter such as potential or current representing, respectively, the instant Cartesian coordinates of the position of a point or object I with respect to axes X and Y. The voltages Ex and Ey may be derived from any source such as the D- tentiometers 3 and 4 energized by transformer TR operated from a. voltage ie, having a phase which serves as reference for the system. The secondary of transformer TR deliver voltages :E and :FE which have potentials of equal magnitude but of opposite instant polarity. The voltages i-E and :FE are impressed on potentiometers 3 and 4 having slidably adjustable brushes 33v and 34 for respectively selecting voltages Ex and Ey from said potentiometers to represent the Cartesian position coordinates of point or object I with respect to axes X and Y. If the potentiometers are so shaped that the potentials or currents at the brushes change as linear param- 'eters with the position of said brushes, the brush setting will be directly proportional. to Cartesian position coordinates and the instant phase of the voltage Ex and Ey will correspond to the quadrant position ofthe point I.

With the connections shown in Fig. 1, the windings 25 'and 25' will respectively haveinduced in them, voltages En and E., each having a, parameter, such as potential or current representing, as above described, the range and azimuth control voltages. It is to be clearly understood that the connections between windings may be reversed with equally satisfactory operation, that is, the voltages Ex and Ey may be impressed on the movable windings 25 and 25', whereupon the voltages En and E@ are derived from the stationary coils 25 and 26. Although the voltages induced in the secondary windings 25 and 25' are used as control voltages for Cartesian-to-polar conversion in the present instance, it will be apparent that these voltages are actually in quadrature relation as are the voltages in the primary windings 25 and 26', the effect of relative rotation of the quadrature windings being to shift lthe axes to which the induced quadrature voltages `may be referred through the angle of relative rotation, such as the angle 6.

Gears 1, 8, and 2| connect shaft 2 in unity ratio to shaft 6 to which is attached the charting surface 5. Pen I3 charts the course of the moving point or object I by indicating or recording the path thereof on chart 5. Shaft 6 also positions the azimuth responsive unit 36 of the signailing mechanism of the trainer. The details of this azimuth responsive unit of the signal controlling device are described in my United States Patent No. 2,494,508, dated January 10, 1950, but these details are not essential to the understanding or operation of the present invention.

A servo-motor I2, having rotor 35 is adapted to drive shaft 6 through gears 22, 23, 8, 2U and The motor I2 may conveniently be a twophase motor having a winding 29 energized from the reference source of voltage ie, and a quadrature winding 23' energized from ampliiler Il according to the amplitude and phase of the control voltage E. derived from winding 25 of the rotary transformer 9. The amplifier I0 includes the necessary 90 phase shifting circuit as is well known to be required for operation of the 2-phase motor I2. While a two-phase motor is shown in the drawing, it will be ,apparent to those skilled in this art, that a direct current motor may be employed for this purpose by using a demodu-y lator-amplier at III, and similarly, there may be substituted any of numerous other forms of reversible motive devices which are responsive to an alternating voltage such as E having phase and potential as varying parameters.

It will be clear from the above, that with suitable polarization of servo-motor winding 25, the motor I2 will operate in one direction or the other, depending on the phase of E. with respect to the reference phase of the voltage ie, and that chart 5 and shaft 2 will thereby be rotated until the transformer winding 25' is so positioned with respect to windings 25 and 25', energized by Ex and Ey, respectively, that the potential E, is reduced to zero. According to Equation 1 above, the angular position of shaft 6, established by the foregoing servo-action, will then be the -desired azimuth angle 0 representing the direction of the object I from the reference line Y. To prevent hunting of the servo about the reference angle 0, the servo system may be damped by the well-known expedient of deriving an inverse velocity feedback voltage from a polyphase generator operated by motor I2 and applying this potential as an input to amplifier I0. It is to be understood that while the reference value for the voltage Es has been taken as zero for determining the angle 0 in this description, the curcuit may be adapted to employ some other bias data. by adding an equivalent fixed inverse potential to the input of amplifier I0.

A second servo-motor I5, having rotor 24 and two-phase windings 30 and 30' drives lead screw I5 through gears 3| and 32 to position nut I4 carrying pen I3 or a stylus, insulated contact I4', and connecting member 31 which operates the range unit 38'of the signalling mechanism above referred to. The details of said signalling mechanism are described in my United States Patent No. 2,494,508 dated January 10, 1950 but these details are not necessary to the understanding or operation of the present invention.

Contact I4 selects a voltage from potentiometer I9 in accordance with the distance which nut I4 and stylus I3 are from the origin O. The potentiometer I9 is energized by a voltage 1E: of fixed maximum potential and instantly opposite polarity to 1ER, that is, voltage Er is of l opposite sense to En. Amplifier I8 is a summing amplifier which provides an output current pro-- portional to the algebraic sum of voltages iEn and KEr where K is the ratio of the voltage selected by wiper I4' to 1E. The output of amplier i8 energizes winding 30' which controls the speed and direction of motor I6. Winding 30 is energized from the reference source of voltage ie. It will now be understood that servo-motor I5 will operate to adjust brush I4', the stylus or pen I3 and the signalling mechanism range unit arm 31 until the resultant oi' voltages IER and zKEr is zero which balance point corresponds precisely to the polar range r which the object or point I is from origin O. This servo may also be damped, if desired, by velocity feedback in the well-known manner.

In combination, then, the servo-motors I2 and il controlled by the control voltages :En and and Vx and Vy respectively represent components il., derived from voltages E. and Eyby means of rotarytransi'ormer i, will continuously and instantly move the mechanism including elements I and Il and their associated parts according to the Cartesian coordinate voltages Ex and Ey which have phase and potential as the parameters that are varied to represent all positions of said point i with respect to axes X and Y intersecting at origin 0.

The current in the windings of the rotary transformer is also to be understood as being a parameter which varies in representing different coordinate conditions.-

For the purpose of illustrating vector composition, or resolution, reference is made to Figure 2 wherein X and Y are Cartesian reference axes,

- of voltage along said axes. The resultant oi' said components is Va which makes an angle with respect to the Y axis used as a reference direction. It will be clear that any parameter of a voltage may be represented by the components Vx andVy. For example, the parameters may be potential, current, or resultant phase. The voltages Vx and Vy may be derived by potentiometer apparatus similar to that shown in Figure 1 for deriving voltages Ex and Ey or any other form ot variable electrical meanssuch as Variacs, condensers and the like, may be used for the purpose. The apparatus illustrated in Figure 1 may be employed for composing the vectors Vx and Vy into a resultant voltage Va and a control voltage V., the latter for determining the angle 0. For this purpose the potential Vx is connected to winding-2l instead of the potential Ex. Likewise, the voltage Vy is connected to winding 26' instead of energizing this winding by the voltage Ey.

Operation of the servos i2 and i6 for determining 0 and composing Vx and Vy into a voltage Va and also positioning such elements as shaft i and nut il to represent 0 and the parameter of Va respectively, will be similar to the operation previously described for thedetermination of 0 with En.

Clearly, the apparatus of Fig. l may also be employed to indicate or record any function having polar parameters R and 0, the value of R being expressed as a voltage iea applied to lead I1 for energizing amplifier i8. Simultaneously, a control voltage te. for establishing the value of 0 is impressed on lead 39 to energize amplifier I0. It is to be understood that the voltage e. may be derived from a rotary transformer of the character above described or a rotary transformer having one two-phase winding and one single-phase winding, said windings being rotatable with respect to each other and said twophasev winding being energized by a pair of voltages such as Ex and Ey having a resultant at the angle 0.

Having thus described my invention and having illustrated various modifications thereof, it will be obvious to those skilled in the art, after now understanding my invention, that other changes and modifications may be made therein without departing from the spirit and scope of my invention, and I aim in the appended claims to cover such changes and modifications as are within the scope of the invention.

What I claim is:

l. Apparatus for charting the course of av point, said apparatus being responsive to potentials Ex and Ey representing respectively the instant Cartesian position coordinates of said pointand comprising an azimuth unit and a range unit movable in accordance with equivalent polar'coordinates R and 0 of the point, said coordinate R representing the distance of the point from a reference origin and 0 representing the angle subtended between said point, the origin and a reference direction; means for operating said apparatus comprising an adjustable electromagnetic coordinate conversion device the adjustment of which corresponds to the angle 0, said device being energized by the potentials Ex and Ey for inductively deriving potentials En and E, said potential Ea corresponding to the polar coordinate R and the potential E., varying from a minimum value according to the deviation of the adjustment of said device from the angle 0, means responsive to the control potential E, for changing said adjustment until the potential E. is minimized, an operative connection between said device adjusting means and the azimuth unit to move said azimuth unit in accordance with the angle 0 and means for moving the range unit in accordance with the distance R, said last named means including a servo motor operatively connected tov said range unit and to variable electrical means for deriving a voltage having a parameter varying in accordance with the distance R and in opposite sense to that of potential Ea, and means for controlling said servo motor responsive to the instant values of said last-named voltage and the potential En.

2. Apparatus for charting the course of a moving point, said apparatus being responsive to potentials Ex and Ey representing respectively the instant Cartesian position coordinates of said point and including a charting surface and a stylus associated therewith, means comprising an azimuth servo-motor unit and a range servornotor unit movable in accordance with equivalent polar coordinates R and 0 of the point, said means adapted to produce relative motion between said stylus and surface in accordance with the values of R and 0, said. coordinate R representing the Vdistance of the point from a reference origin and 0 representing the angle subtended between said point, the origin and a reference direction; means for operating said servo-units comprising, a rotary transformer the rotation of which corresponds to the angle 0, said transformer being energized by the potentials Ex and Ey for inductively deriving potentials En and Eg, said potential En corresponding to the polar coordinate R and the potential Eg being a control potential varying from a minimum value according to the deviation of the rotation of said device from the angle 0, an electrical circuit between the transformer and azimuth servo for energizing said azimuth servo in speed and direction of movement according to the voltage Et, variable electrical means for deriving a potential KEl-V in accordance with the movement of the range servo having a polarity opposite to En, and an electronic circuit responsive to the opposing potentials KEr and En for energizingsaid range servo to maintain said range unit at a position producing equilibrium between the effects of said opposcording to the respective parameters of the Ex and E, voltages for inductively deriving a voltage En and a control voltage E9, said voltage En having a parameter corresponding to the value of the polar coordinate R, and said voltage E having a parameter varying from a reference value according to the deviation of the adjustment of said electromagnetic means from the adjustmentvcorresponding to the angle 0, means responsive to the control voltage E@ for changing said adjustment until the parameter of E0 equals said reference value, an azimuth element positioned by the adjusting means responsive to voltage E0, an adjustable range. element and means responsive to the voltage Ea for adjusting said range element corresponding to the distance R, said means for adjusting the range element comprising a servomotor operatively connected to the range element and to variable electrical means for deriving a voltage KEr having a parameter varying in accordance with the range R and in opposite sense to'the parameter of the range representing voltage En, and means for controlling the servomotor comprising a motor` controlcircuit responsive to the instant values of the range representing parameters of the voltages ER and KEr.

RICHARD CARL .1" gv t REFERENCES cri-En The following references are of record in the file of this patent:

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